Multiple μ-stability analysis for memristor-based complex-valued neural networks with nonmonotonic piecewise nonlinear activation functions and unbounded time-varying delays

An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria

The stability analysis of recurrent neural networks (RNNs) with multiple equilibria has received extensive interest since it is a prerequisite for successful applications of RNNs. With the increasing theoretical results on this topic, it is desirable to review the results for a systematical understanding of the state of the art. This article provides an overview of the stability results of RNNs with multiple equilibria including complete stability and multistability. First, preliminaries on the complete stability and multistability analysis of RNNs are introduced. Second, the complete stability results of RNNs are summarized. Third, the multistability results of various RNNs are reviewed in detail. Finally, future directions in these interesting topics are suggested.

Multistability and Stabilization of Fractional-Order Competitive Neural Networks With Unbounded Time-Varying Delays

This article investigates the multistability and stabilization of fractional-order competitive neural networks (FOCNNs) with unbounded time-varying delays. By utilizing the monotone operator, several sufficient conditions of the coexistence of equilibrium points (EPs) are obtained for FOCNNs with concave-convex activation functions. And then, the multiple μ -stability of delayed FOCNNs is derived by the analytical method. Meanwhile, several comparisons with existing work are shown, which implies that the derived results cover the inverse-power stability and Mittag-Leffler stability as special cases. Moreover, the criteria on the stabilization of FOCNNs with uncertainty are established by designing a controller. Compared with the results of fractional-order neural networks, the obtained results in this article enrich and improve the previous results. Finally, three numerical examples are provided to show the effectiveness of the presented results.